Pre-Algebra Examples

$20 \div 2$ , $25$

Step 1

Find the GCF for the numerators $20, 25$ .

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Step 1.1

Find the common factors for the numerical part:

$20, 25$

Step 1.2

The factors for $20$ are $1, 2, 4, 5, 10, 20$ .

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Step 1.2.1

The factors for $20$ are all numbers between $1$ and $20$ , which divide $20$ evenly.

Check numbers between $1$ and $20$

Step 1.2.2

Find the factor pairs of $20$ where $x \cdot y = 20$ .

$\begin{array}{c} x & y \\ 1 & 20 \\ 2 & 10 \\ 4 & 5 \end{array}$

Step 1.2.3

List the factors for $20$ .

$1, 2, 4, 5, 10, 20$

Step 1.3

The factors for $25$ are $1, 5, 25$ .

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Step 1.3.1

The factors for $25$ are all numbers between $1$ and $25$ , which divide $25$ evenly.

Check numbers between $1$ and $25$

Step 1.3.2

Find the factor pairs of $25$ where $x \cdot y = 25$ .

$\begin{array}{c} x & y \\ 1 & 25 \\ 5 & 5 \end{array}$

Step 1.3.3

List the factors for $25$ .

$1, 5, 25$

Step 1.4

List all the factors for $20, 25$ to find the common factors.

$20$ : $1, 2, 4, 5, 10, 20$

$25$ : $1, 5, 25$

Step 1.5

The common factors for $20, 25$ are $1, 5$ .

$1, 5$

Step 1.6

The GCF (HCF) of the numerical factors $1, 5$ is $5$ .

$5$

Step 2

The GCF of a single polynomial is itself.

$2$

Step 3

Determine the GCF for $20 \div 2, 25$ .

$\frac{5}{2}$